Drawing Planar Graphs with a Prescribed Inner Face

  • Tamara Mchedlidze
  • Martin Nöllenburg
  • Ignaz Rutter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8242)


Given a plane graph G (i.e., a planar graph with a fixed planar embedding) and a simple cycle C in G whose vertices are mapped to a convex polygon, we consider the question whether this drawing can be extended to a planar straight-line drawing of G. We characterize when this is possible in terms of simple necessary conditions, which we prove to be sufficient. This also leads to a linear-time testing algorithm. If a drawing extension exists, it can be computed in the same running time.


Plane Graph Convex Polygon Outer Face Simple Cycle Planar Drawing 
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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Tamara Mchedlidze
    • 1
  • Martin Nöllenburg
    • 1
  • Ignaz Rutter
    • 1
  1. 1.Institute of Theoretical InformaticsKarlsruhe Institute of Technology (KIT)Germany

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